Can HMM, MRF, or CRF be used to classify the state of a single observation, not the entire observation sequence?
Yes this is possible and is exactly what a Markov process aims to accomplish.

The Hidden Markov Model can be considered a simple dynamic Bayesian network. This means that it will generate a probabilistic outcome for a number of states (classes) given a sequence of inputs.

This can be used for a classification task based on a threshold probability to make a confirmed decision.

Let's take a simple example



The above example is a model to determine  how a person will be feeling given some sample data of the previous days.



# Sample data
data = ['Healthy', 'Healthy', 'Fever']


Using this data, it's possible to calculate the probability of each possible state (outcome).



# Probability after 2 Healthy and 1 Fever day
P = 0.6 * 0.7 * 0.3

# Final day state 'Fever'
# Calculating probabilities for each state
Dizzy  = P * 0.6
Cold   = P * 0.3
Normal = P * 0.1


We can calculate the probability of each state and this will be unique for every unique sequence of historical data.